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Description: The average price per square foot for a home in a large county in a certain state is $225. The council of a country town wonders if the mean price of the homes in their town is less than the mean price of the homes in the county. The town council sel

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The average price per square foot for a home in a large county in a certain state is $225. The council of a country town wonders if the mean price of the homes in their town is less than the mean price of the homes in the county. The town council selected a random sample of 9 homes that have recently sold in their town. They found the price per square foot and want to perform a hypothesis test at the α=0.01 significance level. The data is listed below.

221.4 213.1 219.1 229.6 220.7 224.4 221.6 217.8 223.9

1. Calculate the test statistic and the P-value. Include the sample Statistics.

2. What is the decision at the given significance level?

3. What do you conclude?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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